Question

Find the equation of a parabola with vertex on the line y=x, axis parallel to 0x, and passing through (6,-2),(3,4).

Answer 1

@geerky42

Answer 2

never seen an equation like this

Answer 3

wow tough question.

Answer 4

give me min

Answer 5

this is probably my assignment

Answer 6

and i have exam tommorow lol

Answer 7

I don't think such parabola exists.

Answer 8

https://www.desmos.com/calculator/ivqqpnqxih

Answer 9

Do you have answer?

Answer 10

i have its \[y^2-4x-4y+12=0: 5y^2-36x-28y+140=0\]

Answer 11

huh, problem said axis of symmetry is parallel to x=0?

Answer 12

can you help me to factor this,
\[55x^2-72x+84\]

Answer 13

so parabola must be vertical? I am confused

Answer 14

do you know site that can factor that out?

Answer 15

or its not factorable?

Answer 16

It's not factorable

Answer 17

Let A( h, h ) be the vertex.

Since the axis of symmetry is parallel to OX,

the equation of this parabola is

( y - h )² = 4a ( x - h ) .................... (1)
.........................................

Since it passes through the points

( 6, -2 ) and ( 3, 4 ),

(-2-h)² = 4a(6-h) ........... (2)

(4-h)² = 4a(3-h) ............. (3)

Dividing EQ(1) by EQ(2),

(2+h)² / (4-h)² = (6-h) / (3-h).

Solving this will give you h.

Put this value of h in (2) to get a.

Then, put these values of a and h

in (1) to get the final answer.

Answer 18

Because it has no real root

Answer 19

its from google

Answer 20

Dividing EQ(1) by EQ(2),

(2+h)² / (4-h)² = (6-h) / (3-h).
how to work with this?

Answer 21

Exactly what does OX mean?

Answer 22

IDK, D:

Answer 23

Not really sure. Your problems is kind of abusive.

Answer 24

But I would expand everything, then multiply both sides by denominator, then combine like terms.

Answer 25

ah I get it.

Answer 26

how?

Answer 27

gee I wrote a lot of LaTeX and Openstudy crashes.. all time wasted

Answer 28

I'm just write on paper then post it, is that ok to you?

Answer 29

yup,i will appreciate it more if you do :D

Answer 30

ok tahes me time, is that ok?

Answer 31

it would takes me time*

Answer 32

if you write it, can you try this problem too...

find the point of intersection of the given curves and draw the figure
\[x^2= 4y, x^2=y+3\]

Answer 33

Ok, there is good chance I won't be here when you wake up, so I seriously pray these papers make a difference.

For \(\dfrac{(2+h)^2}{(4-h)^2}=\dfrac{6-h}{3-h}\):

Answer 34

And for point of intersection problem:

Answer 35

grr forgot to rotate photos. so here are them again:

Answer 36

For figures from same problem:

https://www.desmos.com/calculator/qbsw1ybtnw